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Register a new userDecay behaviors of Pc hadronic molecules
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The $P_c(4380)$ and $P_c(4450)$ states observed recently by LHCb experiment were proposed to be either $bar{D} Sigma_c^*$ or $bar{D}^* Sigma_c$ S-wave bound states of spin parity $J^P={frac32}^-$. We analyze the decay behaviors of such two types of hadronic molecules within the effective Lagrangian framework. With branching ratios of ten possible decay channels calculated, it is found that the two types of hadronic molecules have distinguishable decay patterns. While the $bar{D} Sigma_c^*$ molecule decays dominantly to $bar{D}^* Lambda_c$ channel with a branching ratio by 2 orders of magnitude larger than to $bar{D}Lambda_c$, the $bar{D}^* Sigma_c$ molecule decays to these two channels with a difference of less than a factor of 2. Our results show that the total decay width of $P_c(4380)$ as the spin-parity-${frac32}^-$ $bar{D} Sigma_c^*$ molecule is about a factor of 2 larger than the corresponding value for the $bar{D}^* Sigma_c$ molecule. It suggests that the assignment of $bar{D} Sigma_c^*$ molecule for $P_c(4380)$ is more favorable than the $bar{D}^* Sigma_c$ molecule. In addition, $P_c(4450)$ seems to be a $bar{D}^* Sigma_c$ molecule with $J^P={frac52}^+$ in our scheme. Based on these partial decay widths of $P_c(4380)$, we estimate the cross sections for the reactions $gamma p to J/psi p $ and $ pi pto J/psi p $ through the s-channel $P_c(4380)$ state. The forthcoming $gamma p$ experiment at JLAB and $pi p$ experiment at JPARC should be able to pin down the nature of these $P_c$ states.
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In this proceeding, we present our recent work on decay behaviors of the $P_c$ hadronic molecules, which can help to disentangle the nature of the two $P_c$ pentaquark-like structures. The results turn out that the relative ratio of the decays of $P^+_c(4380)$ to $bar{D}^* Lambda_c$ and $J/psi p$ is very different for $P_c$ being a $bar D^*Sigma_c$ or $bar DSigma_c^*$ bound state with $J^P=frac{3}{2}^-$. And from the total decay width, we find that $P_c(4380)$ being a $bar DSigma_c^*$ molecule state with $J^P=frac{3}{2}^-$ and $P_c(4450)$ being a $bar D^*Sigma_c$ molecule state with $J^P=frac{5}{2}^+$ is more favorable to the experimental data.
There are eighteen possibly existing $D^{(*)} bar D^{(*)}$, $D^{(*)} bar K^{(*)}$, and $D^{(*)} D_s^{(*)-}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in $B$ and $B^*$ decays through the current algebra, and calculate their relative branching ratios through the Fierz rearrangement, as summarized in Table III. Our results support the interpretations of the $X(3872)$, $Z_c(3900)$, $Z_c(4020)$, and $X_0(2900)$ as the molecular states $D bar D^*$ of $J^{PC} = 1^{++}$, $D bar D^*$ of $J^{PC} = 1^{+-}$, $D^* bar D^*$ of $J^{PC} = 1^{+-}$, and $D^* bar K^*$ of $J^P = 0^{+}$, respectively. Our results also suggest that the $Z_{cs}(3985)$, $Z_{cs}(4000)$, and $Z_{cs}(4220)$ are strange partners of the $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$, respectively. In the calculations we estimate the lifetime of a weakly-coupled composite particle $A = |BCrangle$ to be $1/t_A approx 1/t_B + 1/t_C + Gamma_{A to BC} + cdots$, with $cdots$ partial widths of other possible decay channels.
Many efforts have been made to reveal the nature of the overabundant resonant structures observed by the worldwide experiments in the last two decades. Hadronic molecules attract special attention because many of these seemingly unconventional resonances are located close to the threshold of a pair of hadrons. To give an overall feature of the spectrum of hadronic molecules composed of a pair of heavy-antiheavy hadrons, namely, which pairs are possible to form molecular states, we take charmed hadrons for example to investigate the interaction between them and search for poles by solving the Bethe-Salpeter equation. We consider all possible combinations of hadron pairs of the $S$-wave singly-charmed mesons and baryons as well as the narrow $P$-wave charmed mesons. The interactions, which are assumed to be meson-exchange saturated, are described by constant contact terms which are resummed to generate poles. It turns out that if a system is attractive near threshold by the light meson exchange, there is a pole close to threshold corresponding to a bound state or a virtual state, depending on the strength of interaction and the cutoff. In total, 229 molecular states are predicted. The observed near-threshold structures with hidden-charm, like the famous $X(3872)$ and $P_c$ states, fit into the spectrum we obtain. We also highlight a $Lambda_cbar Lambda_c$ bound state that has a pole consistent with the cross section of the $e^+e^-toLambda_cbar Lambda_c$ precisely measured by the BESIII Collaboration.
The spectrum of hadronic molecules composed of heavy-antiheavy charmed hadrons has been obtained in our previous work. The potentials are constants at the leading order, which are estimated from resonance saturation. The experimental candidates of hadronic molecules, say $X(3872)$, $Y(4260)$, three $P_c$ states and $P_{cs}(4459)$, fit the spectrum well. The success in describing the pattern of heavy-antiheavy hadronic molecules stimulates us to give more predictions for the heavy-heavy cases, which are less discussed in literature than the heavy-antiheavy ones. Given that the heavy-antiheavy hadronic molecules, several of which have strong experimental evidence, emerge from the dominant constant interaction from resonance saturation, we find that the existence of many heavy-heavy hadronic molecules is natural. Among these predicted heavy-heavy states we highlight the $DD^*$ molecule and the $D^{(*)}Sigma_c^{(*)}$ molecules, which are the partners of famous $X(3872)$ and $P_c$ states. Quite recently, LHCb collaboration reported a doubly charmed tetraquark state, $T_{cc}$, which is in line with our results for the $DD^*$ molecule. With the first experimental signal of this new kind of exotic states, the upcoming update of the LHCb experiment as well as other experiments will provide more chances of observing the heavy-heavy hadronic molecules.
In recent years data have been accumulated at various experiments about states in the heavy quarkonium mass range that seem to be inconsistent with the most simple variants of the quark model. In this contribution it is demonstrated that most of those data are consistent with a dominant molecular nature of those states. It is also discussed which kind of observables are sensitive to the molecular component and which are not.
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